In recent years, various types of medical procedures have been developed which involve the connection of various fluid tubes between the patient and various instruments including sources of fluid pumped into the patient and suction lines to remove fluid from the patient. All of this development activity has produced a need for a valving mechanism and delivery conduit which can be securely held and controlled by one hand, leaving the other hand free to perform other functions. Since these mechanisms necessarily must be low-cost disposable mechanisms, the conventional prior art designs will not satisfy the requirements for several reasons. The prior art devices are usually too complex and costly to be thrown away when they are contaminated with body fluids. Also, the prior art devices are typically unwieldly and difficult to hold and control with one hand. An example of a prior art medical valve is shown in U.S. Pat. No. 4,568,332 issued to Ronald D. Shippert Feb. 4, 1986. The Shippert valve, which is designed for use in suction lipectomy, is made from metal and is fabricated from a multitude of parts which must be assembled together in a complex assembly system.